Turkey on Monday said that the wanted partner of one of the gunmen behind the terror attacks in France crossed into Syria last week, insisting it was not at fault for failing to detain her.

Turkish Foreign Minister Mevlut Cavusoglu said Hayat Boumeddiene had crossed into Syria on January 8, the same day that her partner Amedy Coulibaly is suspected of shooting dead a policewoman outside Paris on the second day of the Paris attacks.

"She entered Turkey on January 2 from Madrid. There are images of her at the airport," Mr Cavusoglu was quoted as saying by state-run news agency Anatolia.

"Then she crossed into Syria on January 8. This is clear from the telephone records."

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Hayat Boumeddiene (right) presenting her passport at Sabiha Gokcen airport in Istanbul on January 2.Credit:AFP

Turkish television channel Haber Turk later broadcast images of a woman it said was Boumeddiene crossing the Turkish border at passport control at Sabiha Gokcen airport in Istanbul.

Wearing a headscarf, she was accompanied by a bearded, unidentified man in the security footage.

Mr Cavusoglu said the 26-year-old Boumeddiene, who had married Coulibaly in an Islamic ceremony, stayed at a hotel in the Kadikoy district on the Asian side of Istanbul and was accompanied by another person.

He did not give further details on the identity of the other individual and did not make clear if she had travelled to Syria on her own.

Hayat Boumeddiene is believed to have fled to Syria.Credit:Getty Images

'No warning from France'

But Turkish officials insisted that they were not at fault for allowing her to enter and then leave Turkey unapprehended after a week on its territory, saying they had not been warned in a timely fashion by France.

Mr Cavusoglu added that Turkey passed the information to the French authorities "even before they asked for it" as soon as Ankara identified her whereabouts.

"We told them: 'The person you are looking for was here, stayed here and crossed into Syria illegally'," he said.

Interior Minister Efkan Ala also said Turkey did not refuse Boumeddiene entry because French authorities had made no such request and that they hadn't warned Ankara that she was "dangerous."

He added that Turkey's intelligence agency, the National Intelligence Organisation (MIT), and the police were still working to shed more light on the matter.

Western countries have long accused Turkey of not doing enough to stem the flow of jihadists seeking to join IS fighters in neighbouring Syria.

But Ankara insists it has now stepped up border security and has repeatedly said the West also has a responsibility to share intelligence.

Speaking in Berlin, Turkish Prime Minister Ahmet Davutoglu said that Turkey made an "extraordinary effort" to ensure security along its 911 kilometre (566 mile) border with Syria.

'Under surveillance'

The statements confirm that Boumeddiene was already outside France when the three-day killing spree began, contrary to earlier speculation that she had been involved in the attacks which claimed 17 lives.

The killings began on January 7 when brothers Cherif and Said Kouachi stormed the Paris offices of French satirical weekly Charlie Hebdo, slaughtering 12 people.

Coulibaly on January 9 took hostages at a kosher supermarket in eastern Paris which was then raided by police in the evening. The gunman and four hostages were killed. The Kouachi brothers were also killed after a separate hostage-taking incident.

A man resembling Coulibaly claimed to be a member of the Islamic State (IS) jihadist group in a posthumous video released online on Sunday.

Turkey's Yeni Safak newspaper reported that MIT took action following reports that Boumeddiene was in Turkey and put her under surveillance due to her "suspicious behaviour".

She stayed at the hotel in the Kadikoy for two days with a man named Mahdi Sabri and left the hotel only twice during her stay, Yeni Safak said.

The last signal received from her phone showed that she was in the Syrian town of Tel Abyad, the daily said. This would mean she would likely have crossed from around the town of Akcakale on the Turkish side of the border.

Press reports have speculated that she may have joined IS jihadists who have captured swathes of Iraq and Syria right up to the Turkish border.